A. This is the maximum achievable sales growth rate without needing to purchase any new fixed assets. However, this is not the maximum achievable growth rate without needing any additional external financing.

B. The company's fixed assets are presently being used at 85% of their capacity to generate sales of $100,000. If they were being used at 100% of their capacity, sales would be $100,000 ÷ .85, which is $117,647. Therefore, any sales growth rate of up to $17,647 ÷ $100,000, or 17.65%, would not require the purchase of additional fixed assets.

The next step is to calculate the maximum sales growth rate that can be achieved with no external financing assuming no additional fixed assets are purchased. We will then compare the first growth rate with the second growth rate. The lower of the two rates will be the answer to the question.

Cash, accounts receivable and inventory will increase at the same rate, which we will call "g". We are assuming that net fixed assets will not increase at all, and the problem tells us that held-to-maturity securities will not change. Accounts payable and accrued liabilities will also increase at rate g. Since the goal is no new external financing, notes payable and long-term debt will not increase at all.

The amount of external financing needed will be the amount of increase in assets minus the amount of increase in liabilities minus the increase in retained earnings. Therefore, the equation we will be working with is:

Increase in Assets - Increase in Liabilities - Increase in Retained Earnings = 0

We set the equation equal to zero because we want the external financing needed to be zero.

Increase in Assets = Total Current Assets of $43,500 × g, where g is the growth rate in sales.

Increase in Liabilities =  (Accounts Payable of $3,000 + Accrued Liabilities of $6,000) × g, or $9,000 × g.

The Increase in Retained Earnings is a little more complicated.  Since borrowings and invested funds will not be changing, we will assume that the net interest expense from last year will not change, either. It will remain $1,200. So we will begin with EBIT of $6,200 and we will say that that will increase by g. So EBIT for next year will be $6,200 + ($6,200 × g).

Since interest expense will be $1,200, EBT next year will be $6,200 + $6,200g - $1,200, which can be simplified to $5,000 + $6,200g.

The tax rate is .35. Therefore, the amount of EBT not paid out in tax will be 1 - .35, which is .65.

Therefore, Net Income After Tax will be .65 × ($5,000 + $6,200g), which simplifies to $3,250 + $4,030g.

Dividends last year were $975, and the company's dividend policy is to increase dividends by 4% per year,

regardless of how much net income changes. Therefore, dividends next year will be $975 × 1.04, or $1,014.

So our addition to retained earnings for next year will be $3,250 + $4,030g - $1,014, which simplifies to $2,236 + $4,030g.

So our equation will be:

43,500g - 9,000g - (2,236 + 4030g) = 0

Solving for g, we get:

30,470g - 2,236 = 0

30,470g = 2,236

g = .0734, or 7.34%

Next, we compare the rate of sales growth that can be achieved without purchasing any new fixed assets (17.65%) with the rate assuming no new fixed assets are purchased (7.34%). Since the second rate (7.34%) is lower than the first (17.65%), the second rate is the answer to the question.

We can prove this by calculating what the increase in assets, the increase in liabilities, and the increase in retained earnings would be at a growth rate of 7.34%, as follows:

The increase in assets is $43,500 × .0734, or $3,193.

The increase in liabilities is $9,000 × .0734, or $661.

The increase in retained earnings will require constructing a pro forma income statement. We will calculate the income statement amounts by multiplying the past year's amounts by 1.0734.

                 PRO FORMA INCOME STATEMENT       

                 Net sales                $100,000 × 1.0734     $107,340 

                 Cost of goods sold         $66,200 × 1.0734       71,059 

                 Gross profit                                  $ 36,281 

                 Selling expense            $16,400 × 1.0734      17,604 

                 General & admin. expense   $11,200 × 1.0734      12,022 

                 EBIT                                         $ 6,655 

                 Net interest expense   Same as last year            1,200 

                 EBT                                         $ 5,455 

                 Taxes @ 35%                                   1,909 

                 Net income                                   $ 3,546 

                 Minus: dividends            $975 × 1.04           1,014 

                 Addition to retained earnings                     $ 2,532 

The increase in retained earnings is $2,532.

We can now plug all of these figures into our equation, which is:

Increase in Assets - Increase in Liabilities - Increase in Retained Earnings = 0

$3,193 - $661 - $2,532 = 0, so the equation is true, and the maximum achievable sales growth rate without the need for additional external financing is 7.34%.

C. This answer results from assuming that all current assets and all current liabilities will grow at the same rate, the rate of sales growth. Only current assets, accounts payable and accrued liabilities will grow at the rate of sales growth.

See the correct answer for a full explanation.

D. This answer results from assuming that all assets and all liabilities will grow at the same rate, the rate of sales growth. Only current assets, accounts payable and accrued liabilities will grow at the rate of sales growth. See the correct answer for a full explanation.